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Pile-foundation system shock loading in an axisymmetric approach

Vestnik MGSU 8/2015
  • Vasenkova Ekaterina Viktorovna - Moscow State University of Civil Engineering (National Research University) (MGSU) Senior Lecturer, Department of Higher Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zuev Vladimir Vasil’evich - Moscow State Institute of Radio Engineering, Electronics and Automation (MIREA Doctor of Physical and Mathematical Sciences, Professor, chair, Department of Applied Mathematics and Informatics, Moscow State Institute of Radio Engineering, Electronics and Automation (MIREA, 20 Stromynka str., Moscow, 107996, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 101-108

The basic problem of structural mechanics, namely the problem of pile shock loading sunk in a foundation, has been examined in an axisymmetric approach within defining relations for irreversible deformations offered earlier in the space of deformations. As a model of the theory of plasticity, the Mises model generalized by the authors has been accepted, the use of which solves a nonstationary system of nine two-dimensional equations with various entry and boundary conditions. Enlightened attitudes use approximate engineering approaches which allow estimating the behavior of a pile-foundation system. A solution is constructed mainly with the use of the theory of linear-elastic continuum. However they do not enable to consider various peculiarities of deformation behavior of soils and pile materials and to give an appropriate detailed picture of a system mode of deformation. Mechanical peculiarities of the behavior of foundation and pile materials discovered recently demand more enlightened attitudes to analyze a mode of deformation in a pile-foundation system considering both plasticity and fracture. The offered approach enables to give a complete picture of a mode of deformation in a pile-foundation system at any time and a picture of occurrence and development of plasticity and fracture zones.

DOI: 10.22227/1997-0935.2015.8.101-108

References
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  3. Ter-Martirosyan Z.G., Ala Said Mukhammed Abdul Malek, Ter-Martirosyan A.Z., Ainbetov I.K. Napryazhenno-deformirovannoe sostoyanie dvukhsloynogo osnovaniya s preobrazovannym verkhnim sloem [Stress-Strain State of a double-layer foundation with a transformed upper layer]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2008, no. 2, pp. 81—95. (In Russian)
  4. Zuev V.V., Shmeleva A.G. Osesimmetrichnoe udarnoe nagruzhenie uprugoplasticheskoy sredy s razuprochneniem i peremennymi uprugimi svoystvami [Axisymmetric Shock Loading of an Elasto-Plastic Medium with Softening and Variable Elastic Properties]. Vestnik Samarskogo gosudarstvennogo universiteta : Estestvennonauchnaya seriya [Vestnik of Samara State University : Natural Sciences]. 2007, no. 2 (52), pp. 100—106. (In Russian)
  5. Zuev V.V., Shmeleva A.G. Modelirovanie povedeniya sloistykh zashchitnykh pregrad pri dinamicheskikh nagruzkakh [Modeling of the Behavior for Stratified Protective Barriers at Dynamic Loads]. Promyshlennye ASU i kontrollery [Industrial Automatic Control Systems and Controllers]. 2009, no. 12, pp. 28—30. (In Russian)
  6. Zuev V.V., Shmeleva A.G. Nekotorye aktual’nye zadachi dinamicheskogo nagruzheniya uprugoplasticheskikh sred s uslozhnennymi svoystvami [Some Current Problems of Dynamic Loading for Elasto-Plastic Media with Complicated Properties]. Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo [Vestnik of Lobachevsky University of Nizhni Novgorod]. 2011, no. 4 (5), pp. 2189—2191. (In Russian)
  7. Shmeleva A.G. Udarnoe nagruzhenie plasticheskikh sred [Shock Loading of Plastic Media]. LAP Lambert Academic Publishing, 2012, 128 p. (In Russian)
  8. Mata M., Casals O., Alcal J. The Plastic Zone Size in Indentation Experiments: The Analogy with the Expansion of a Spherical Cavity. Int. J. of Solids and Structures. 2006, vol. 43, no. 20, pp. 5994—6013. DOI: http://dx.doi.org/10.1016/j.ijsolstr.2005.07.002.
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  16. Frishter L.Yu. Raschetno-eksperimental’nyy metod issledovaniya napryazhenno-deformiruemogo sostoyaniya sostavnykh konstruktsiy v zonakh kontsentratsii napryazheniy [Computational and Experimental Method of Stress-Strain State Investigation of Composite Structures in the Areas of Stress Concentration]. Stroitel’naya mekhanika inzhenernykh konstruktsiy sooruzheniy [Structural Mechanics of Engineering Constructions and Buildings]. 2008, no. 2, pp. 20—27. (In Russian)
  17. Frishter L.Yu., Mozgaleva M.L. Sopostavlenie vozmozhnostey chislennogo i eksperimental’nogo modelirovaniya napryazhenno-deformiruemogo sostoyaniya konstruktsiy s uchetom ikh geometricheskoy nelineynosti [Comparison of Capabilities of Numerical and Experimental Simulation for Stress-Strain State of Structures Subject to their Geometric Nonlinearity]. International Journal for Computational Civil and Structural Engineering. 2010, vol. 6, no. 1—2, pp. 221—222. (In Russian)
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  20. Antonov V.I. Napryazheniya v rulone pri dopolnitel’nom natyazhenii lenty [Stresses inside a Roll in Case of Higher Belt Tension]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 10, pp. 24—29. (In Russian)
  21. Zuev V.V. Opredelyayushchie sootnosheniya i dinamicheskie zadachi dlya uprugoplasticheskikh sred s uslozhnennymi svoystvami [Defining Relations and Dynamic Problems for Elasto-Plastic Media with Complicated Properties]. Moscow, Fizmatlit Publ., 2006, 176 p. (In Russian)

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Essential FEM statements applied to structural mechanics problems. Part 1

Vestnik MGSU 11/2014
  • Ignat’ev Aleksandr Vladimirovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 37-57

In the article, the author shares his classification of FEM statements that may serve as a guide in respect of the huge number of works that are published and being published with a view to the FEM efficiency improvement. The author provides a summarized history of the finite element method, and classifies its configurations and versions. The author also provides FEM statements applicable to the deflection method. Derivation of the rigidity matrix designated for shaft-based finite elements is demonstrated in the article. The author employs one-dimensional framing as an example aimed to demonstrate the convergence of the FEM method in terms of deflections, if the finite element grid is refined. However it is also noteworthy that in the event of a fine grid, the finite element designed for plates does not coincide with the finite element of a thin plate designed as the initial physical model. However, the system of equations, provided by the author, takes account of the influence produced by the load onto the finite element and generates the exact solution irrespective of any finite values of the length that are equal to the physical model of a finite element.

DOI: 10.22227/1997-0935.2014.11.37-57

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  51. Bathe K.-J., Wilson E.L. Numerical Methods in Finite Element Analysis. New Jersey, Prentice-Hall, 1976, 528 p.
  52. Bathe K.-Yu. Metody konechnykh elementov [Finite Elements Methods]. Transl. Into Russian. Moscow, FIZMATLIT Publ., 2010, 1024 p.
  53. Bathe K.J. Finite Element Procedures. Prentice Hall, Englewood Cliffs, 1996, 1036 p.
  54. Bathe K.J., Wilson E.L. Numerical Methods in Finite Element Analysis. Prentice-Hall Inc., New Jersey, 1976.
  55. Vasidzu K. Variatsionnye metody v teorii uprugosti i plastichnosti [Variation Methods in Plasticity Theory]. Moscow, Mir Publ., 1987, 542 p. (In Russian).
  56. Gallager R. Metod konechnykh elementov. Osnovy [Finite Element Method. Basics]. Moscow, Mir Publ., 1984, 428 p. (In Russian).
  57. Zenkevich O.K., Morgan K. Konechnye elementy i approksimatsiya [Finite Elements and Approximation]. Moscow, Mir Publ., 1986, 318 p. (In Russian).
  58. Morrey D.O. O skhodimosti resheniy v metode konechnykh elementov [On Solutions’ Convegence in Finite Element Method]. Raketnaya tekhnika i kosmonavtika [Rocket Enineering and Space Technologies]. 1970, no. 4, pp. 112—114. (In Russian).
  59. Bazeley G.P., Cheung Y.K., Irons B.M., Zienkiewicz O.C. Triangular Elements in Plate Bending — Conforming and Non-conforming Solutions. Proc. Conf. On Matrix Methods in Structural Mechanics. Air Force Inst. of Tech., Wright Patterson A. F. Base, Ohio, 1965, pp. 547—576.
  60. Marchuk G.I., Agoshkov V.I. Vvedenie v proektsionno-setochnye metody [Introduction into Projective Grid Methods]. Moscow, Nauka Publ., 1981, 416 p. (In Russian).
  61. Zenkevich O.K. Metod konechnykh elementov v tekhnike [Finite Element Method in Technology]. Transl. into Russian. Moscow, Mir Publ., 1975, 541 p.
  62. Ignat’ev V.A. Metod konechnykh elementov v zadachakh stroitel’noy mekhaniki [Finite Element Method in Problems of Structural Mechanics]. Saratov, Saratov University Publ., 1980, 87 p. (In Russian).
  63. Chuvikovskiy V.S. Chislennye metody raschetov v stroitel’noy mekhanike korablya [Numerical Calculation Methods in Structural Mechanics of Ships]. Leningrad, Sudostroenie Publ., 1976, 376 p.

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Main formulations of the finite element method for the problems of structural mechanics. Part 2

Vestnik MGSU 12/2014
  • Ignat’ev Aleksandr Vladimirovich - Volgograd State University of Architecture and Civil Engineering (VSUACE) Candidate of Technical Sciences, Associate Professor, Department of Structural Mechanics, Volgograd State University of Architecture and Civil Engineering (VSUACE), 1 Akademicheskaya str., Volgograd, 400074, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 40-59

The author offers a classification of Finite Element formulations, which allows orienting in a great number of the published and continuing to be published works on the problem of raising the efficiency of this widespread numerical method. The second part of the article offers examination of straight formulations of FEM in the form of displacement approach, area method and classical mixed-mode method. The question of solution convergence according to FEM in the form of classical mixed-mode method is considered on the example of single-input single-output system of a beam in case of finite element grid refinement. The author draws a conclusion, that extinction of algebraic equations system of FEM in case of passage to the limit is not a peculiar feature of this method in general, but manifests itself only in some particular cases. At the same time the obtained results prove that FEM in mixed-mode form provides obtaining more stable results in case of finite element grid refinement in comparison with FEM in the form of displacement approach. It is quite obvious that the same qualities will appear also in two-dimensional systems.

DOI: 10.22227/1997-0935.2014.12.40-59

References
  1. Gorodetskiy A.S., Zavoritskiy V.I., Lantukh-Lyashñhenko A.I., Rasskazov A.O. Metod konechnykh elementov v proektirovanii transportnykh sooruzheniy [Finite Element Method in Transport Constructions Design]. Moscow, Transport Publ., 1981, 143 p. (In Russian)
  2. Postnov V.A., Kharkhurim I.Ya. Metod konechnykh elementov v raschetakh sudovykh konstruktsiy [Finite Element Method in Ship Structures Calculation]. Leningrad, Sudostroenie Publ., 1974, 344 p. (In Russian)
  3. Sekulovich M. Metod konechnykh elementov [Finite Element Method]. Translated from Serbian Yu.N. Zueva, editor V.Sh. Barbakadze. Moscow, Stroyizdat Publ., 1993, 664 p. (In Russian)
  4. Ignat’ev A.V. Osnovnye formulirovki metoda konechnykh elementov v zadachakh stroitel’noy mekhaniki. Chast’ 1 [Essential FEM Statements Applied to Structural Mechanics Problems. Part 1]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 11, pp. 37—57. (In Russian)
  5. Bogner F., Fox R., Schmit L. A Cylindrical Shell Discrete Element. AIAA. 1967, vol. 5, no. 4, pp. 745—750. DOI: http://dx.doi.org/10.2514/3.4056.
  6. Allman D.J. Treugol’nye konechnye elementy dlya rascheta izgibaemykh plastin pri postoyannykh i lineyno raspredelennykh izgibayushchikh momentakh [Trigonal Finite Elements for Bending Plates Calculation in Case of Permanent and Linearly Distributed Bending Moments]. Raschet uprugikh konstruktsiy s ispol’zovaniem EVM [Calculation of Elastic Structures Using Computer]. Translated from English, editor A.P. Filin. Leningrad, Sudostroenie Publ., 1974, pp. 80—101. (In Russian)
  7. Klochkov Yu.V. Razvitie teorii lineynogo i nelineynogo deformirovaniya obolochek na osnove MKE s uchetom smeshcheniya kak zhestkogo tselogo i izmeneniya tolshchiny [Development of the Theory of Linear and Non-linear Deformation of Shells Basing on FEM with Account for the Displacement as Stiff Entire and Change of the Width]. Dissertation of the Doctor of Technical Sciences. Volgograd, Volgogradskaya GSKhA Publ., 2001, 326 p. (In Russian)
  8. Bathe K.-J., Wilson E.L. Numerical Methods in Finite Element Analysis, New Jersey, Prentice-Hall, 1976, 528 p.
  9. Bathe K. Metody konechnykh elementov [Finite Elements Methods]. Transl. from English by V.P. Shidlovskiy. Moscow, FIZMATLIT Publ., 2010, 1024 p. (In Russian)
  10. Tsybenko A.S. Primenenie treugol’nykh trekhuzlovykh nesoglasovannykh elementov dlya resheniya osesimmetrichnykh zadach teorii uprugosti [Application of Trigonal Nonconforming Elements for Solving Axisymmetric Tasks of Elasticity Theory]. Problemy plastichnosti [Elasticity Problems]. 1986, no. 3, pp. 79—83.
  11. Semenov V.A., Semenov P.Yu. Hybrid Finite Elements for Analysis of Shell Structures. Proc. International Congress ICSS—98, 22—26 June 1998, Moscow, Russia. Moscow, 1998, vol. 1, pp. 244—251.
  12. Bathe K.J. Finite Element Procedures. Prent. Hall, Englewood Cliffs, 1996, 1036 p.
  13. Fraeijs de Veubeke B., Sander G. An Equilibrium Model for Plate Bending. International J. Solids and Structures. 1968, vol. 4, no. 4, pp. 447—468. DOI: http://dx.doi.org/10.1016/0020-7683(68)90049-8.
  14. Tyukalov Yu.A. Reshenie zadach stroitel’noy mekhaniki metodom konechnykh elementov v napryazheniyakh na osnove funktsionala dopolnitel’noy energii i printsipa vozmozhnykh peremeshcheniy [Solving the Tasks of Structural Mechanics by Finite Element Method in Strains Basing on Additional Energy Functional and Principle of Possible Sisplacements]. Dissertation of the Doctor of Technical Sciences. Kirov, VyatGY Publ., 2006, 314 p. (In Russian)
  15. Ignat’ev V.A., Ignat’ev A.V., Zhidelev A.V. Smeshannaya forma metoda konechnykh elementov v zadachakh stroitel’noy mekhaniki [Mixed Form of Finite Element Method in Problems of Structural Mechanics]. Volgograd, VolgGASU Publ., 2006, 172 p. (In Russian). (In Russian)
  16. Ignat’ev A.V., Gabova V.V. Algoritm staticheskogo rascheta ploskikh sterzhnevykh sistem po metodu konechnykh elementov v smeshannoy forme [Algorithm of Static Analysis of Flat Truss Structures Using Finite Element Method in Mixed Mode Form]. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel’nogo universiteta. Seriya: Estestvennye nauki [Proceedings of Volgograd State University of Architecture and Civil Engineering. Series: Natural Sciences]. 2007, no. 6 (23), pp. 72—77. (In Russian)
  17. Rekunov S.S., Voronkova G.V. Osobennosti rascheta plastinok po metodu konechnykh elementov v smeshannoy forme [Features of Calculating Plates Using Finite Elements Method in Mixed-Mode Form]. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel’nogo universiteta. Seriya: Stroitel’stvo i arkhitektura [Proceedings of Volgograd State University of Architecture and Civil Engineering. Series: Construction and Architecture]. 2007, no. 7 (26), pp. 74—77. (In Russian)
  18. Maslennikov A.M. Raschet stroitel’nykh konstruktsiy chislennymi metodami [Calculation of Building Structures Using Numerical Methods]. Leningrad, LGU Publ., 1987, 224 p. (In Russian)
  19. Pokrovskiy A.A. Smeshannaya forma MKE v raschetakh sterzhnevykh sistem i sploshnoy sredy [Mixed-Mode Form of FEM in Calculation of Truss Systems and Continuous Medium]. Dissertation of the Doctor of Technical Sciences. Penza, PGASA Publ., 2000, 308 p. (In Russian)

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The history and development prospects of one of the methods for solving multidimensional problems of structural mechanics

Vestnik MGSU 12/2015
  • Stankevich Anatoliy Nikolaevich - Kyiv National University of Construction and Architecture (KNUCA) Candidate of Technical Sciences, Associate Professor, chair, Department of Strength of Materials, Kyiv National University of Construction and Architecture (KNUCA), 31 Vozdukhoflotskiy prospekt, Kiev, 03680, Ukraine; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 76-91

The equations describing stress-strain state of the majority of the calculation models in linear statement are considered in frames of the theory of elasticity (statics and dynamics) and thermoelasticity. These equations are defined in three-dimentional space or with account for symmetry in teo-dimentional space and are belong to complicated tasks of mathematical physics. The famous mathematicians and nechanics had already offered solutions for the simplest cases of such tasks. But it is impossible to solve the majority of tasks, especially the dynamic ones, using analythical solutions. In this work the authors deal with the modern methods for solving multidimensional problems of structural mechanics. The attention is paid to the methods of dimension reduction of the initial equations. The development and improvement of the method of lines is considered in detail, the shortcomings of the existing approaches are enumerated and the possible development direction of the method to the new task classes is offered.

DOI: 10.22227/1997-0935.2015.12.76-91

References
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  2. Lyav A. Matematicheskaya teoriya uprugosti [Mathematical Theory of Elasticity]. Translated from English. Moscow, Leningrad, ONTI Publ., 1935, 674 p.
  3. Novatskiy V. Dinamicheskie zadachi termouprugosti [The Dynamic Thermoelasticity Problems]. Translated from Polish. Moscow, Mir Publ., 1970, 256 p. (In Russian)
  4. Kruz T., Ritstso F. Metod granichnykh integral’nykh uravneniy. Vychislitel’nye aspekty i prilozheniya v mekhanike : sbornik trudov [The Method of Boundary Integral Equations. Computational Aspects and applications on Mechanics : Collection of Works]. Translated from English. Moscow, Mir Publ., 1978, no. 15, 210 p. (Novoe v zarubezhnoy nauke. Mekhanika [New in the Foreign Science. Mechanics]) (In Russian)
  5. Veryuzhskiy Yu.V. Metod potentsiala v staticheskikh zadachakh stroitel’noy mekhaniki : dissertatsiya ... doktora tekhnicheskikh nauk [Potential Methods for Static Problems of Structural Mechanics. Dissertation of the Doctor of Technical Sciences]. Kiev, 1980, 431 p. (In Russian)
  6. Veryuzhskiy Yu.V. Chislennye metody potentsiala v nekotorykh zadachakh prikladnoy mekhaniki [Numerical Methods of Potential in Some Problems of Applied Mechanics]. Kiev, Vishcha shkola Publ.,1978, 183 p. (In Russian)
  7. Benerdzhi P., Batterfild R. Metod granichnykh elementov v prikladnykh naukakh [The Method of Boundary Elements in Applied Sciences]. Translated from English. Moscow, Mir Publ., 1984, 494 p. (In Russian)
  8. Brebbiya K., Uoker S. Primenenie metoda granichnykh elementov v tekhnike [Application of the Method of Boundary Elements in Engineering]. Moscow, Mir Publ., 1982, 248 p. (In Russian)
  9. Vaynberg D.V., Sinyavskiy A.L. Raschet obolochek [Calculation of Shells]. Kiev, Gosstroyizdat USSR Publ., 1961, 119 p. (In Russian)
  10. Kupradze V.D. O priblizhennom reshenii zadach matematicheskoy fiziki [Approximate Solution of the Problems of Mathematical Physics]. Uspekhi matematicheskikh nauk [Success of Mathematical Sciences]. 1967, vol. 22, no. 2 (134), pp. 59—107. (In Russian)
  11. Parton V.Z., Perlin P.I. Integral’nye uravneniya teorii uprugosti [Integral Equations of Elasticity Theory]. Moscow, Nauka Publ., 1977, 312 p. (In Russian)
  12. Ugodchikov A.G., Khutoryanskiy N.M. Metod granichnykh elementov v mekhanike deformiruemogo tverdogo tela [Boundary Element Method in Solid Mechanics]. Kazan, Izdatel’stvo Kazanskogo universiteta Publ., 1986, 295 p. (In Russian)
  13. Lur’e A.I. K teorii tolstykh plit [On the Theory of Thick Plates]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1942, vol. 6, no. 2—3, pp. 151—168. (In Russian)
  14. Kil’chevskiy N.A. Obobshchenie sovremennoy teorii obolochek [Generalization the Modern Theory of Shells]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1939, vol. 2, no. 4, pp. 427—438. (In Russian)
  15. Vlasov V.Z. Metod nachal’nykh funktsiy v zadachakh teorii uprugosti [The Method of Initial Functions in the Axisymmetric Problem of the Theory of Elasticity]. Izvestiya’ AN SSSR, OTN. [News of the Academy of Sciences of the USSR. Technical Sciences]. 1955, no. 7, pp. 49—69. (In Russian)
  16. Selezov І.T. Doslіdzhennya poperechnikh kolivan’ plastin [Oscillations Research of Transverse Plates]. Prikladna mekhanіka [Applied Mechanics]. 1960, vol. 6, no. 5, pp. 319—326. (In Ukrainian)
  17. Selezov I.T., Kil’chitskaya G.A. Privedenie trekhmernoy dinamicheskoy zadachi termouprugosti dlya sloya postoyannoy tolshchiny [Bringing the Three-Dimensional Dynamic Thermoelasticity Problem for a Layer of Constant Thickness]. Teplovye napryazheniya v elementakh konstruktsiy : doklady nauchnogo soveshchaniya [Thermal Stresses in Structural Elements : Reports of the Scientific Conference]. Kiev, Naukova dumka Publ., 1964, no. 4, pp. 172—179. (In Russian)
  18. Vorovich I.I. Nekotorye matematicheskie voprosy teorii plastin i obolochek [Some Mathematical Problems in the Theory of Plates and Shells]. Trudy Vtorogo Vsesoyuznogo s”ezda po teoreticheskoy i prikladnoy mekhanike [Works of the Second All-Union Meeting on Theoretical and Applied Mechanics]. Moscow, Nauka Publ., 1966, no. 3, pp. 116—136. (In Russian)
  19. Vorovich I.I., Malkina O.S. Napryazhennoe sostoyanie tolstoy plity [Stress State of a Thick Plate]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1967, vol. 31, no. 2, pp. 230—241. (In Russian)
  20. Vorovich I.I., Prokopov V.K. Nekotorye voprosy trekhmernoy teorii uprugosti [Some Questions of the Three-Dimensional Theory of Elasticity]. III Vsesoyuznyy s”ezd po teorii i prikladnoy mekhanike. Annotatsiya dokladov [The 3rd All-Union Meeting on the Theory and Applied Mechanics. Annotation of Reports]. Moscow, Nauka Publ., 1968, p. 81. (In Russian)
  21. Vlasov V.V. Primenenie metoda nachal’nykh funktsiy k raschetu tolstykh plit [Application of the Method of Initial Functions to the Calculation of Thick Plates]. Issledovaniya po teorii sooruzheniy : sbornik [Investigations on Structural Analysis : Collection]. Moscow, Gosstroyizdat Publ., 1961, no. 10, pp. 189—207. (In Russian)
  22. Vlasov V.V. Metod nachal’nykh funktsiy v osesimmetrichnoy zadache teorii uprugosti [The Method of Initial Functions in the Theory of Elasticity]. Raschet plastin i obolochek [Calculation of Plates and Shells]. 1963, no. 34, pp. 31—45. (In Russian)
  23. Vlasov V.Z., Leont’ev N.N. Balki, plity i obolochki na uprugom osnovanii [Beams, Plates and Shells on the Elastic Foundation]. Moscow, Fizmatgiz Publ., 1960, 491 p. (In Russian)
  24. Gol’denveyzer A.L. Postroenie priblizhennoy teorii izgiba plastinki metodom asimptoticheskogo integrirovaniya uravneniy teorii uprugosti [An Approximate Theory of Bending a Plate Using the Method of Asymptotic Integration of the Equations of Elasticity Theory]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1962, vol. 26, no. 4, pp. 668—686. (In Russian)
  25. Gol’denveyzer A.L. Asimptoticheskiy metod postroeniya teorii obolochek [The Asymptotic Method of Constructing the Theory of Shells]. Materialy I Vsesoyuznoy shkoly po teorii i chislennym metodam rascheta obolochek i plastin [Materials of the 1st All-Russian School on the Theory and Numerical Methods of Calculating Shells and Plated]. Tbilisi, Izdatel’stvo Tbilisskogo universiteta Publ., 1975, pp. 151—213. (In Russian)
  26. Vekua I.N. Teoriya tonkikh pologikh obolochek peremennoy tolshchiny [The Theory of Thin Shallow Shells of Variable Thickness]. Trudy Tbilisskogo matematicheskogo instituta [Works of the Tbilisi Mathematical Institute]. Tbilisi, Metsniereba Publ., 1965. T. 30. 103 p. (In Russian)
  27. Akhiezer V.G. Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s ney [Classical Moment Problem and Some Related Questions in Analysis]. Moscow, Fizmatgiz Publ., 1961, 310 p.
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  29. Vekua I.N. Nekotorye obshchie metody postroeniya razlichnykh variantov teorii obolochek [Some Common Methods of Constructing Different Versions of the Theory of Shells]. Moscow, Nauka Publ., 1982, 288 p. (In Russian)
  30. Isakhanov G.V., Chibiryakov V.K., Smolyar A.M. Chislenno-analiticheskiy metod resheniya zadach statiki tolstykh neodnorodnykh plastin [Numerical-Analytical Method for Solving Statics Problems of Thick Inhomogeneous Plates]. Trudy 13-y Vsesoyuznoy konferentsii po teorii plastin i obolochek [Works of the 13th All-Russian Conference on the Theory of Plates and Shells]. Tallin, 1983, part 2, pp. 130—135. (In Russian)
  31. Isakhanov G.V., Chibiryakov V.K. Razvitie metoda Vekua I.N. v statike i dinamike tolstykh plastin [Development of the Method of I.N. Vekua in Statics and Dynamics of Thick Plates]. Tezisy dokladov 2-y Vsesoyuznoy konferentsii po teorii uprugosti [Abstracts of the 2nd All-Union Conference on Elasticity Theory]. Tbilisi, 1984, 122 p. (In Russian)
  32. Chibiryakov V.K. Obobshchennyy metod konechnykh integral’nykh preobrazovaniy v statike i dinamike netonkikh plastin [Generalized Method of Integral Transformations in Statics and Dynamics of Non-Thin Plates]. Soprotivlenie materialov i teoriya sooruzheniy : respublikanskiy mezhvedomstvennyy nauchnyy sbornik [Strength of Materials and Theory of Structures : Republican Interdepartmental Scientific Collection]. Kiev, Budivel’nik Publ., 1982, no. 40, pp. 90—95. (In Russian)
  33. Chibiryakov V.K., Smolyar A.M. Ob odnom obobshchenii metoda konechnykh integral’nykh preobrazovaniy v teorii tolstykh plastin [On a Generalization of the Method of Integral Transformations in the Theory of Thick Plates]. Soprotivlenie materialov i teoriya sooruzheniy : respublikanskiy mezhvedomstvennyy nauchnyy sbornik [Strength of Materials and Theory of Structures : Republican Interdepartmental Scientific Collection]. Kiev, Budivel’nik Publ., 1983, no. 42, pp. 80—86. (In Russian)
  34. Chibіryakov V.K., Smolyar A.M. Teorіya tovstikh plastin ta obolonok [The Theory of Thick Plates and Shells]. Cherkasi, ChDTU Publ., 2002, 160 p. (In Ukrainian)
  35. Chibiryakov V.K. Ob odnom variante uravneniy tsilindricheskogo izgiba netonkikh plastin [On a Variant of the Cylindrical Bending Equations of Non-Thin Plates]. Soprotivlenie materialov i teoriya sooruzheniy : respublikanskiy mezhvedomstvennyy nauchnyy sbornik [Strength of Materials and Theory of Structures : Republican Interdepartmental Scientific Collection]. Kiev, Budivel’nik Publ., 1977, no. 31, pp. 59—67. (In Russian)
  36. Chibiryakov V.K. Chislennoe reshenie zadach statiki i dinamiki tolstykh plastin [Numerical Solution of the Problems of Statics and Dynamics of Thick Plates]. Chislennye metody resheniya zadach stroitel’noy mekhaniki : sbornik nauchnykh statey [Numerical Methods of Solcing the Problems of Structural Mechanics : Collection of Scientific Articles]. Kiev, KISI Publ., 1978, pp. 153—157. (In Russian)
  37. Chibіryakov V.K., Zhupanenko І.V. Vlasnі kolivannya tovstoї tsilіndrichnoї obolonki [Own Fluctuations of Thick Cylindrical Shell]. Opіr materіalіv і teorіya sporud : naukovo-tekhnіchniy zbіrnik [Resistance of Materials and Theory of Structures : Scientific and Technical Collection]. Kiev, KNUBA Publ., 2009, no. 84, pp. 127—133. (In Ukrainian)
  38. Chibіryakov V.K., Zhupanenko І.V. Vlasnі kolivannya tovstostіnnoї obolonki obertannya zmіnnoї tovshchini [Proper Rotation Oscillation of a Thick Shell of Variable Thickness]. Promislove budіvnitstvo ta іnzhenernі sporudi [Industrial Construction and Engineering Structures]. 2010, no. 2, pp. 5—9. (In Ukrainian)
  39. Chibіryakov V.K., Zhupanenko І.V. Metodika rozv’yazannya zadachі pro vlasnі kolivannya plastin obertannya zmіnnoї tovshchini [Methods for Solving the Problem of the Oscillations of Plates of Variable Thickness]. Opіr materіalіv і teorіya sporud : naukovo-tekhnіchniy zbіrnik [Resistance of Materials and Theory of Structures : Scientific and Technical Collection]. Kiev, KNUBA Publ., 2010, no. 86, pp. 30—46. (In Ukrainian)
  40. Chibіryakov V.K., Zhupanenko І.V. Pro odin algoritm rozrakhunku vіsesimetrichnikh kolivan’ krugloї plastini [On One Algorithm of Axially Symmetric Vibrations of Circular Plates]. Opіr materіalіv і teorіya sporud : naukovo-tekhnіchniy zbіrnik [Resistance of Materials and Theory of Structures : Scientific and Technical Collection]. Kiev, KNUBA Publ., 2007, no. 81, pp. 43—50. (In Ukrainian)
  41. Chibiryakov V.K., Boyko K.E. Opredelenie chastot i form sobstvennykh kolebaniy po utochnennym teoriyam plastin [Definition of Frequencies and Forms of Natural Oscillations in Refined Theories of Plates]. Soprotivlenie materialov i teoriya sooruzheniy : respublikanskiy mezhvedomstvennyy nauchnyy sbornik [Strength of Materials and Theory of Structures : Republican Interdepartmental Scientific Collection]. Kiev, Budivel’nik Publ., 1985, no. 47, pp. 74—80. (In Russian)
  42. Chibiryakov V.K., Boyko K.E. Osesimmetrichnye sobstvennye kolebaniya tolstykh plastin peremennoy tolshchiny [Axisymmetric Eigenmodes of Thick Plates of Variable Thickness]. Soprotivlenie materialov i teoriya sooruzheniy : respublikanskiy mezhvedomstvennyy nauchnyy sbornik [Strength of Materials and Theory of Structures : Republican Interdepartmental Scientific Collection]. Kiev, Budivel’nik Publ., 1986, no. 49, pp. 54—58. (In Russian)
  43. Kantorovich L.V. Odin pryamoy metod priblizhennogo resheniya zadachi o minimume dvoynogo integrala [One Direct Method for the Approximate Solution of the Problem of the Minimum of a Double Integral]. Izvestiya AN SSSR. Seriya 7. Otdelenie matematicheskikh i estestvennykh nauk [News of the Academy of Sciences of the USSR. Series 7. Department of Mathematical and Natural Sciences]. 1933, no. 5, pp. 647—652. (In Russian)
  44. Sadskul M.N.O., Obiozor C.N. A Simple Introduction to the Method of Lines. International Journal of Electrical Engineering Education. 2000, vol. 37/3, pp. 282—296.
  45. Vinokurov L.P. Reshenie prostranstvennoy zadachi teorii uprugosti v peremeshcheniyakh [Solution of the Spatial Problem of Elasticity in Displacements]. Byulleten’ Khar’kovskogo inzhenerno-stroitel’nogo instituta [Bulletin of Kharkov Engineering and Construction Institute]. 1940, no. 18. (In Russian)
  46. Slobodyanskiy M.G. Sposob priblizhennogo integrirovaniya uravneniy s chastnymi proizvodnymi i ego primenenie k zadacham teorii uprugosti [The Method of Approximate Integration of Partial Differential Equations and Its Application to the Problems of the Theory of Elasticity]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1939, vol. 3, no. 1, pp. 75—82. (In Russian)
  47. Faddeeva V.N. Metod pryamykh v primenenii k nekotorym kraevym zadacham [Method of Lines Applied to Some Boundary Problems]. Trudy matematicheskogo instituta imeni V.A. Steklova [Works of the Mathematical Institute Named after V.A. Steklov]. 1949, vol. XXVIII, pp. 73—103. (In Russian)
  48. Kantorovich L.V., Frumkin P.V. Primenenie odnogo metoda priblizhennogo resheniya uravneniy v chastnykh proizvodnykh k resheniyu zadachi o kruchenii prizmaticheskikh sterzhney [On the Application of a Method for the Approximate Solution of Partial Differential Equations and the Problem of Torsion of Prismatic Bars]. Trudy Leninigradskogo instituta inzhenerov promyshlennogo stroitel’stva [Works of the Leningrad Institute of Industrial Construction Engineers]. 1937, no. 4, pp. 111—112. (In Russian)
  49. Slobodyanskiy M.G. Prostranstvennye zadachi teorii uprugosti dlya prizmaticheskikh tel [Spatial Problem of Elasticity Theory for Prismatic Bodies]. Uchenye zapiski Moskovskogo gosudarstvennogo universiteta. Mekhanika [Scientific Notes of the Moscow State University. Mechanics]. 1940, no. 39. (In Russian)
  50. Slobodyanskiy M.G. Otsenka pogreshnosti iskomoy velichiny pri reshenii lineynykh zadach variatsionnym metodom [Errors Estimate for the Unknown Quantity in the Solution of Linear Problems Using the Variational Method]. DAN SSSR [Reports of the Academy of Sciences of the USSR]. 1952, vol. 86, no. 2, pp. 243—246. (In Russian)
  51. Slobodyanskiy M.G. Otsenki pogreshnosti priblizhennogo resheniya v lineynykh zadachakh, svodyashchayasya k variatsionnym, i ikh primenenie k opredeleniyu dvustoronnikh priblizheniy v staticheskikh zadachakh teorii uprugosti [Errors Estimation of Approximate Solutions to Linear Problems, which are Reduced to the Variationals and their Application to the Determination of Two-sided Approximations for Static Problems of Elasticity]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1952, vol. 16, no. 4, pp. 449—464. (In Russian)
  52. Slobodyanskiy M.G. Otsenka pogreshnostey priblizhennykh resheniy lineynykh zadach [Errors Estimation of Approximate Solutions of Linear Problems]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1953, vol. 17, no. 2, pp. 229—244. (In Russian)
  53. Slobodyanskiy M.G. O priblizhennom reshenii lineynykh zadach, svodyashchikhsya k variatsionnym [On the Approximate Solution of Linear Problems Reduced to Variationals]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1953, vol. 17, no. 5, pp. 623—626. (In Russian)
  54. Slobodyanskiy M.G. Priblizhennoe reshenie nekotorykh kraevykh zadach dlya ellipticheskogo deferentsial’nogo uravneniya i otsenka pogreshnosti [Approximate Solution of Some Boundary Value Problems for Elliptic Deferential Equation and Error Estimate]. DAN SSSR [Reports of the Academy of Sciences of the USSR]. 1953, vol. 89, no. 2. (In Russian)
  55. Slobodyanskiy M.G. O preobrazovanii problemy minimuma funktsionala k probleme maksimuma [On the Transformation of the Problem of Functional Minimum to the Problem of Maximum]. DAN SSSR [Reports of the Academy of Sciences of the USSR]. 1953, vol. 91,no. 4, pp. 733—736. (In Russian)
  56. Slobodyanskiy M.G. O postroenii priblizhennogo resheniya v lineynykh zadachakh [On the Construction of Approximate Solutions to Linear Problems]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1955, vol. 19, no. 5. (In Russian)
  57. Vinokurov L.P. Pryamye metody resheniya prostranstvennykh i kontaktnykh zadach dlya massivov i fundamentov [Direct Methods for Solving Spatial and Contact Problems for Soils and Foundations]. Kharkov, KhGU Publ., 1956, 280 p. (In Russian)
  58. Vinokurov L.P. Raschet plit na uprugom poluprostranstve s primeneniem inzhenerno-diskretnogo metoda [Calculation of Plates on Elastic Half-Space Using Integro-Discrete Method]. Vestnik inzhenerov i tekhnikov [Proceedings of Engineers and Technicians]. 1951, no. 4, pp. 166—171. (In Russian)
  59. Vinokurov L.P. Priblizhennye metody resheniya differentsial’nykh uravneniy stroitel’noy mekhaniki [Approximate Methods for Solving Differential Equations of Structural Mechanics]. Trudy KhISI [Works of Kharkov Institute of Construction and Engineering]. 1951, no. 3. (In Russian)
  60. Vinokurov L.P. Raschet kolodtsa na uprugom osnovanii, nagruzhennogo silami, ne lezhashchimi v ploskosti krivizny kolodtsa [Calculation of a Well on an Elastic Foundation Loaded with the Forces That Do Not Lie in the Plane of the Well Curvature]. Vestnik inzhenerov i tekhnikov [Proceedings of Engineers and Technicians]. 1938, no. 1. (In Russian)
  61. Vinokurov L.P. Priblizhennyy metod resheniya ploskikh zadach teorii uprugosti [An Approximate Method of Solving Plane Elasticity Problems]. Trudy KhISI [Works of Kharkov Institute of Construction and Engineering]. 1949, vol. II. (In Russian)
  62. Petrov Yu.P. Raschet na izgib uprugikh pryamougol’nykh plastin diskretnym metodom [Discrete Method Calculation of Bending of Orthotropic Elastic Plates]. Trudy Khar’kovskogo aviatsionnogo instituta [Works of Kharkov Aviation Institute]. 1961, no. 18, pp. 86—99. (In Russian)
  63. Petrov Yu.P. Osnovy rascheta na izgib plastin diskretnym metodom [Bases of Bending Calculation of Plates Using Discrete Method]. Trudy Khar’kovskogo aviatsionnogo instituta [Works of Kharkov Aviation Institute]. 1961, no. 18, pp. 67—83. (In Russian)
  64. Petrov Yu.P. Raschet na izgib kosozashchemlennoy konsol’noy plastiny peremennoy tolshchiny [Bending Calculation of Sidely Restrained Console Plate of Variable Thickness]. Trudy Khar’kovskogo aviatsionnogo instituta [Works of Kharkov Aviation Institute]. 1963, no. 22, pp. 62—78. (In Russian)
  65. Petrov Yu.P. Raschet na izgib diskretnym metodom ortotropnykh uprugikh plastin [Bending Calculation of Orthotropic Elastic Using Discrete Method]. Trudy Khar’kovskogo aviatsionnogo instituta [Works of Kharkov Aviation Institute]. 1963, no. 22, pp. 79—86. (In Russian)
  66. Petrov Yu.P. Raschet na izgib plastin s lineynym izmeneniem tolshchiny diskretnym metodom [Bending Calculation of Plates with Linear Variation of Thickness Using Discrete Method]. Trudy Khar’kovskogo aviatsionnogo instituta [Works of Kharkov Aviation Institute]. 1961, no. 18, pp. 79—86. (In Russian)
  67. Shkelev L.T. Ispol’zovanie metoda pryamykh dlya resheniya bigarmonicheskogo uravneniya [Using the Method of Lines for Solving Biharmonic Equation]. Referativnaya informatsiya o zakonchenykh nauchno-issledovatel’skikh rabotakh v VUZakh USSR. Stroitel’naya mekhanika, raschet sooruzheniy : sbornik [Reference Information on the Concluded Scientific and Research Works in the Higher Institutions of the USSR. Structural Mechanics, Calculation of Structures : Collection]. Kiev, Vyshcha shkola Publ., 1971, no. 2. (In Russian)
  68. Shkelev L.T. Raschet plastin proizvol’noy formy v polyarnykh koordinatakh. Ploskoe izgibnoe napryazhennoe sostoyanie [Calculation of Plates of Arbitrary Forms in Polar Coordinates. Flat Bending Stress State]. Referativnaya informatsiya : sbornik [Reference Information : Collection]. 1971, no. 2. (In Russian)
  69. Shkelev L.T. Reshenie kraevoy zadachi dlya bigarmonicheskogo uravneniya metodom pryamykh v polyarnykh koordinatakh [Solution of the Boundary Problem for Biharmonic Equation by the Method of Lines in Polar Coordinates]. Referativnaya informatsiya : sbornik [Reference Information: Collection]. 1972, no. 3. (In Russian)
  70. Korbakov A.F. Razvitie i primenenie metoda pryamykh k issledovaniyu slozhnogo napryazhennogo i deformirovannogo sostoyaniya plastin i plastinchatykh sistem : dissertatsiya ... doktora tekhnicheskikh nauk [Development and Application of the Method of Lines to Study Complex Stress and Strain State of Plates and Plate Systems. Dissertation of the Doctor of Technical Sciences]. Kiev, 1985. (In Russian)
  71. Morskov Yu.A. Raschet izgibaemykh plastin proizvol’noy formy [Calculation of Bent Plates of Arbitrary Shape]. Referativnaya informatsiya o zakonchenykh nauchno-issledovatel’skikh rabotakh v VUZakh USSR. Stroitel’naya mekhanika, raschet sooruzheniy : sbornik [Reference Information on the Concluded Scientific and Research Works in the Higher Institutions of the USSR. Structural Mechanics, Calculation of Structures : Collection]. Kiev, 1977, no. 9. (In Russian)
  72. Morskov Yu.A. Reshenie nekotorykh zadach izgiba dvukhsvyaznykh plastin proizvol’nogo ochertaniya [Solution of Some Bending Problems of Doubly Connected Plates of Arbitrary Shape]. Soprotivlenie materialov i teoriya sooruzheniy : sbornik [Strength of Materials and Theory of Structures : Collection]. Kiev, Budіvel’nik Publ., 1977, no. 31. (In Russian)
  73. Morskov Yu.A. Primenenie metoda pryamykh v polyarnykh koordinatakh k resheniyu zadach izgiba plastin proizvol’noy formy [Application of the Method of Lines in Polar Coordinates for the Problems of Bending Plates of Arbitrary Shape]. Soprotivlenie materialov i teoriya sooruzheniy : sbornik [Strength of Materials and Theory of Structures : Collection]. Kiev, Budіvel’nik Publ., 1979, no. 34. (In Russian)
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SCIENTIFIC APPROACHES TO CALCULATION AND DESIGN OF LARGE-SPAN STRUCTURES

Vestnik MGSU 2/2017 Volume 12
  • Sysoeva Elena Vladimirovna - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Buildings and Constructions Design, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 131-141

The article presents the four stages of creation and development of the theory of plate and shell which led to the development of a mechanism of calculation of spatial structures of large span buildings and constructions on an advanced level. Each of the stages of the unique buildings calculation method development includes a description of the main achievements in the sphere of structural mechanics, the theory of elasticity and resistance of materials which became the basis for the modern theory of calculation of plates and shells. In the first stage the fundamentals of solid mechanics were developed; this is presented in works of such outstanding scientists as G. Galilei, J.-L. Lagrange, R. Hooke, L. Euler, Kirchhoff, A. Law etc. Development of the theory of plate and shell would be impossible without these works. But absence of such construction material as reinforced concrete did not enable engineers and architects to create a thin roof. Thickness of coverings was intuitively overstated to ensure durability of buildings. The second stage is interesting by formulation of the general theory of calculation of plate and shell and by transition from the working state analysis of structures to the limit state analysis. Beginning of use of reinforced concrete resulted in decrease of a roof thickness to the diameter of its base, compared to buildings made of stone and brick. The third stage is characterized by development of computational systems for calculation of strength, stability and oscillations of core and thin-walled spatial structures based on the finite element method (FEM). During this period a design of buildings and constructions with spans over 200 m with the use of metal was begun. Currently, or during the fourth stage, structures with the use of metal and synthetic materials for spans up to 300 meters are designed. Calculations of long-span buildings and structures are performed using FEM and taking into account different types of nonlinearity. Each stage selected from the history of construction is exemplified by completed projects, hereat characteristics of roofs indicating the applied construction material are given. Transition from natural stone to concrete, metal and synthetic materials in construction of large-span buildings is illustrated in the table. At the end of each stage the scientists’ and designers’ main achievements in the sphere of science, construction and engineering education are shown.

DOI: 10.22227/1997-0935.2017.2.131-141

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